I have to admit, even after long study of Toole's Confederacy of Dunces, there are some aspects of the tale that are still beyond my understanding. One has been Ignatius Reilly's fascination with destruction and apocalypse. I think I now have the beginning of a connection, and it is tied to the phrase "wrong theology and geometry." According to the interview that Robert Byrne gave to Carmine Palumbo, Toole got that phrase from Byrne, and Byrne got it from H.P. Lovecraft (see the discussion of this in my paper Evidence of influences on John Kennedy Toole's "A Confederacy of Dunces," including Geoffrey Chaucer, page 7 in version 2.0).
I personally have never read H.P. Lovecraft. However, in the December 18, 2014, New York Review of Books, Charles Baxter has an essay discussing Lovecraft in relation to the new annotated volume of Lovecraft's writings. The essay is freely available online at this URL: http://www.nybooks.com/articles/archives/2014/dec/18/hideous-unknown-hp-lovecraft
The passage from the essay that caught my eye and made me think of a deeper connection to Ignatius Reilly was this one: "As for Lovecraft, who died in 1937 at the age of forty-six, he never really grew up. 'Adulthood is hell,' he once wrote in a letter." That certainly describes Ignatius Reilly. And Reilly fantasizes about violence and destruction, much like a goth fan of Lovecraft. I could say more, but I don't want to write your paper for you.
Thesis: Discuss the psychology of Ignatius Reilly in comparison to the themes present in the works of H.P. Lovecraft.